物理学中经典理论的非对易扩展
Non-commutative extensions of classical theories in physics
摘要：
我们提出了一个简短的介绍性概述几个经典物理理论的非交换扩展。经过一般性的讨论的原因表明，非交换性是一个主要的问题，最终将导致统一的重力与其他基本相互作用，我们显示的例子，非交换的推广已知的几何形状。最后，我们讨论了代数的一般性质，可以成为一般化的光滑函数的代数Minkowskian（黎曼）流形，需要描述的量子引力。
英文摘要：
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead to the unification of gravity with other fundamental interactions, we display examples of non-commutative generalizations of known geometries. Finally we discuss the general properties of the algebras that could become generalizations of algebras of smooth functions on Minkowskian (Riemannian) manifolds, needed for the description of Quantum Gravity.
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